Distributed Convex Optimization in the Presence of Uncertainty

Numerous problems in statistics, machine learning and decision making can be cast as (uncertain) convex optimization problems. Coming to large-scale optimization problems, it is important to develop algorithms capable of solving the problem in a distributed fashion. In this line of research, we consider a set of processors with limited computation and communications capabilities connected through a network. Each processor has knowledge of an uncertain convex constraint and a common cost known to all processors. The goal of the network is to agree on a decision vector minimizing (or maximizing) the cost while respecting all agents’ constraint by performing local computation and exchanging data with neighbouring processors. We make resource of randomization to handle uncertainty appearing in an arbitrarily complex fashion in the constraints.

M. Chamanbaz, G. Notarstefano, R. Bouffanais, “A Distributed Ellipsoid Algorithm for Uncertain Convex Problems: A Randomized Approach”, In Proc. 56th IEEE Conference on Decision and Control, Melbourne, Australia.

M. Chamanbaz, G. Notarstefano, R. Bouffanais, “Randomized Constraints Consensus for Distributed Robust Linear Programming”, In Proc. 20th IFAC World Congress, Toulouse, France. PDF.

M. Chamanbaz, G. Notarstefano, F. Sasso, and R. Bouffanais.Randomized constraints consensus for distributed robust mixed-integer programming.IEEE Transactions on Control of NetworkSystems, pages 1–1, 2020.